Optical imaging through turbid media has various applications from long range observations through turbulence to imaging inside living tissues [1]}, [2]}, [3]}, [4]}, [5]}. When light propagates through turbid media, the
wavefront is distorted because of the inhomogeneity,
resulting in the degradation of spatial resolution and the reduction of imaging depth. Low-order aberrations due to random fluctuations of refractive index can be overcome by adaptive optics [6]} and turbulence-free ghost imaging [7]},
while the problem becomes intractable for optically opaque media in which strong light scattering scrambles the spatial information conveyed by light fields. Early experiments using holographic imaging [8]} demonstrated that scattering by stationary media does not erase spatial information carried by light fields [9]}. Speckle patterns appear random but are essentially deterministic, and information about the optical input can be retrieved. Recent advances in wavefront shaping exploiting transmission
matrix [10]}, [11]}, [12]}, [13]}, [14]} and optical phase conjugation [15]}, [16]}, [17]}, [18]}, [19]} have realized focusing and imaging through scattering media. However, they are either invasive and require holographic or interferometric measurements or need prior knowledge of the scattering properties of the media. A more recent development taking advantage of the angular correlation of speckle pattern [20]}, [21]}, [22]}, i.e., “memory effect”, enables non-invasive imaging through scattering layers using the auto-correlation of speckle patterns and a phase-retrieval algorithm [23]}, [24]}, [25]}, [26]}. Although these techniques do not depend on the scattering properties of the media, they share some common shortcomings such as the memory-effect range restricts this approach to thin scattering layers, the small single speckle grain requires high-resolution camera to resolve, and the iterative phase-retrieval algorithm suffers from falling into local optimal solution.
